Stewart is perhaps best known for playing First Officer Murdoch in Titanic (1997). In 2005, Stewart was one of many European actors considered for the vacant role of James Bond for the 007 series. In 2008, Stewart starred in the film Ecstasy based on The Undefeated from Irvine Welsh's best-selling novel Ecstasy: Three Tales of Chemical Romance. Stewart was the voice actor and motion caption actor for Shen in the video game Heavenly Sword. Stewart is well known to Only Fools and Horses fans for portraying Dr Robbie Meadows in the hugely popular television series.

Stewart is married and lives in London with his wife, English actress Clare Byam-Shaw, and his two children, Thomas and Eleanor.